Any agent can help you look for rental property throughout San Antonio. I recommend you start looking 4 - 6 weeks prior to your move out date. This will give you an idea of whats out on the market.
Typically, once you submit an application for a rental property, and are approved, you have two weeks in which to occupy the rental.
If you have any questions regarding properties in your desired area and/or want to know more about criteria required for renting, please feel free to give me a call. I'd be glad to help.